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AMG38
1 year ago

The number Column for your Input variables is also the number of input variables. You have a, b and c as input variables, so you need 3 columns for the inputs.

You also have an output x, which is then the fourth column. You don’t need more columns for a truth table first!

The number rows depends on the number of inputs.

That is, in your case you need 2^3 = 8 lines.

You can prefill the cells for the inputs. Start with the first column. Fill half of the rows of this column with a zero, the other half with a 1, see below.

a | b | c | x
-------------
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |

The neighboring columns for b are now treated, but do not change the number after 4, but after 2 lines.

a | b | c | x
-------------
0 | 0 |
0 | 0 |
0 | 1 |
0 | 1 |
1 | 0 |
1 | 0 |
1 | 1 |
1 | 1 |

The column c is also the same, only that you change the number after each line.

a | b | c | x
-------------
0 | 0 | 0 |
0 | 0 | 1 |
0 | 1 | 0 |
0 | 1 | 1 |
1 | 0 | 0 |
1 | 0 | 1 |
1 | 1 | 0 |
1 | 1 | 1 |

The pattern should be clear now. If you look closely at the last table, you can see that you don’t make anything further than counting high starting from zero, in binary numbers.
This structure applies to both circuits because both have 3 inputs. Your table does not refer to a gate of a circuit, but to the entire circuit!

Now look at the state (x) for a circuit for each line. If, for example, the output (x) is at line 1 (where a=0, b=0 and c=0) to 1, then you write into the first line for x is 1 pure, otherwise a zero.

verreisterNutzer
1 year ago
Reply to  AMG38

Thank you.

tunik123
1 year ago

This is correct, but all eight combinations of the input signals must be considered.

I have never seen the notation of the NAND in the first task. I only know how the NOR is described in the second task.

To write NAND/NOR:

or

for a NOR.

And

or

for a NAND.

verreisterNutzer
1 year ago
Reply to  tunik123

But there are only three input signals with 0. What do you mean?

I actually didn’t know how to write NAND and NOR. Do you know more about it?

tunik123
1 year ago

I had now suspected that in the tables you should consider all combinations (also ones).

To write NAND and NOR, I added my answer because the formula editor does not work on comments.

verreisterNutzer
1 year ago

Haha, it’s confusing.

tunik123
1 year ago

Well, that’s the right column in your tables. Whether you’re overwriting x or the whole formula, doesn’t matter.

By the way: The (so far unknown) spelling for the NAND really exists:

https://de.wikipedia.org/wiki/Logikgatter#Type_von_Logikgattern_und_Symbolik

verreisterNutzer
1 year ago

Yes, the thing is that you should set the truth table for the circuit and the circuit has a single state with three inputs = 0, but it can be that I’m wrong.

Which x should stay away?

The right at the red point, which comes out in the end.

tunik123
1 year ago

I thought all 8 combinations were in demand. But I didn’t think of the task;-)

Which x should stay away?

In the first table, I would write the NAND as much as you did with NOR in the second table.

verreisterNutzer
1 year ago

Thank you. So I have to write 2^3 combinations into the truth table. And the x should stay away?